%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL030-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:03 PM UTC 2026
% Result : Unsatisfiable 131.70s 19.82s
% Output : CNFRefutation 131.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of clauses : 111 ( 106 unt; 0 nHn; 23 RR)
% Number of literals : 116 ( 115 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 155 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_top_12) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
cnf(goals_17,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
cnf(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
cnf(dedekind_law_14,axiom,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-1.ax',dedekind_law_14) ).
cnf(goals_18,negated_conjecture,
( join(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,sk2),complement(sk3))) != meet(composition(sk1,sk2),complement(sk3))
| join(meet(composition(sk1,sk2),complement(sk3)),meet(composition(sk1,sk2),complement(composition(sk1,sk3)))) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
cnf(c_0_16,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_17,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_18,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_19,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_21,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_22,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_23,plain,
composition(X1,composition(one,X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_24,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_26,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_27,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_29,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_31,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24]) ).
cnf(c_0_32,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_34,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_35,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_37,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_30]),c_0_32]),c_0_22]) ).
cnf(c_0_39,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_42,negated_conjecture,
join(sk1,one) = one,
goals_17 ).
cnf(c_0_43,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_22]),c_0_34]) ).
cnf(c_0_44,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
join(X1,composition(sk1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28]),c_0_22]),c_0_28]) ).
cnf(c_0_46,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_34]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
join(X1,join(composition(sk1,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_48,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_36]),c_0_22]) ).
cnf(c_0_49,negated_conjecture,
join(X1,complement(join(complement(composition(sk1,X1)),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
join(one,complement(join(complement(sk1),X1))) = one,
inference(spm,[status(thm)],[c_0_49,c_0_17]) ).
cnf(c_0_51,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_52,negated_conjecture,
join(complement(join(complement(sk1),X1)),one) = one,
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
join(X1,join(X2,composition(sk1,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_54,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_31]),c_0_30]),c_0_22]) ).
cnf(c_0_55,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_56,plain,
join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_57,negated_conjecture,
join(complement(join(X1,complement(sk1))),one) = one,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_51,c_0_54]) ).
cnf(c_0_59,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_55,c_0_20]) ).
cnf(c_0_60,negated_conjecture,
join(complement(join(complement(X1),sk1)),one) = join(X1,one),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
converse(join(X1,converse(top))) = top,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_22,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
join(complement(join(X1,sk1)),one) = join(complement(X1),one),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_64,plain,
converse(join(X1,converse(complement(converse(X1))))) = top,
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_65,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
join(complement(join(sk1,X1)),one) = join(complement(X1),one),
inference(spm,[status(thm)],[c_0_63,c_0_22]) ).
cnf(c_0_67,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_64]),c_0_65]) ).
cnf(c_0_68,negated_conjecture,
join(sk1,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_69,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_70,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_62]) ).
cnf(c_0_71,negated_conjecture,
join(complement(converse(complement(converse(sk1)))),one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_32]),c_0_39]) ).
cnf(c_0_72,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_73,negated_conjecture,
join(sk1,join(X1,one)) = join(X1,one),
inference(spm,[status(thm)],[c_0_68,c_0_22]) ).
cnf(c_0_74,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_69,c_0_44]) ).
cnf(c_0_75,negated_conjecture,
converse(join(complement(converse(sk1)),one)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_59]),c_0_72]) ).
cnf(c_0_76,negated_conjecture,
join(complement(sk1),one) = top,
inference(spm,[status(thm)],[c_0_73,c_0_70]) ).
cnf(c_0_77,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_74]) ).
cnf(c_0_78,axiom,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
dedekind_law_14 ).
cnf(c_0_79,negated_conjecture,
join(complement(converse(sk1)),one) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_75]),c_0_65]) ).
cnf(c_0_80,negated_conjecture,
join(zero,complement(join(complement(sk1),complement(one)))) = sk1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_76]),c_0_32]) ).
cnf(c_0_81,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_82,plain,
join(complement(join(complement(X1),X2)),join(X3,complement(join(complement(X1),complement(X2))))) = join(X3,X1),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_83,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_77,c_0_40]) ).
cnf(c_0_84,plain,
converse(composition(converse(X1),converse(X2))) = composition(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_85,plain,
converse(join(composition(X1,X2),composition(X3,X2))) = composition(converse(X2),converse(join(X1,X3))),
inference(spm,[status(thm)],[c_0_16,c_0_41]) ).
cnf(c_0_86,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_87,negated_conjecture,
complement(join(complement(converse(sk1)),complement(one))) = converse(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_79]),c_0_32]),c_0_39]) ).
cnf(c_0_88,negated_conjecture,
complement(join(complement(sk1),complement(one))) = sk1,
inference(rw,[status(thm)],[c_0_80,c_0_39]) ).
cnf(c_0_89,negated_conjecture,
converse(join(X1,composition(X1,converse(sk1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_81]),c_0_59]),c_0_20]) ).
cnf(c_0_90,negated_conjecture,
( join(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,sk2),complement(sk3))) != meet(composition(sk1,sk2),complement(sk3))
| join(meet(composition(sk1,sk2),complement(sk3)),meet(composition(sk1,sk2),complement(composition(sk1,sk3)))) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))) ),
inference(fof_simplification,[status(thm)],[goals_18]) ).
cnf(c_0_91,plain,
join(X1,complement(join(complement(X2),X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_40]),c_0_40]),c_0_22]) ).
cnf(c_0_92,plain,
join(composition(X1,X2),X3) = converse(join(composition(converse(X2),converse(X1)),converse(X3))),
inference(spm,[status(thm)],[c_0_59,c_0_84]) ).
cnf(c_0_93,plain,
converse(join(composition(X1,converse(X2)),converse(composition(X2,X3)))) = composition(X2,converse(join(X1,converse(X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_16]),c_0_20]) ).
cnf(c_0_94,plain,
join(complement(join(complement(X1),complement(X2))),converse(composition(converse(complement(join(complement(X1),complement(X2)))),converse(complement(join(complement(one),complement(composition(X2,converse(X1))))))))) = converse(composition(converse(complement(join(complement(X1),complement(X2)))),converse(complement(join(complement(one),complement(composition(X2,converse(X1)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_28]),c_0_24]),c_0_24]),c_0_84]),c_0_84]) ).
cnf(c_0_95,negated_conjecture,
join(complement(converse(sk1)),complement(one)) = complement(converse(sk1)),
inference(spm,[status(thm)],[c_0_40,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
join(complement(sk1),complement(one)) = complement(sk1),
inference(spm,[status(thm)],[c_0_40,c_0_88]) ).
cnf(c_0_97,negated_conjecture,
join(X1,composition(X1,converse(sk1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_89]),c_0_20]) ).
cnf(c_0_98,negated_conjecture,
( join(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,sk2),complement(sk3))) != meet(composition(sk1,sk2),complement(sk3))
| join(meet(composition(sk1,sk2),complement(sk3)),meet(composition(sk1,sk2),complement(composition(sk1,sk3)))) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))) ),
c_0_90 ).
cnf(c_0_99,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_91,c_0_40]) ).
cnf(c_0_100,plain,
composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_55]),c_0_20]) ).
cnf(c_0_101,negated_conjecture,
composition(sk1,converse(sk1)) = converse(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_40]),c_0_40]),c_0_20]),c_0_20]),c_0_28]),c_0_22]),c_0_96]),c_0_40]),c_0_59]),c_0_20]),c_0_97]),c_0_40]),c_0_20]),c_0_20]),c_0_28]),c_0_22]),c_0_96]),c_0_40]),c_0_81]) ).
cnf(c_0_102,negated_conjecture,
( join(complement(join(complement(composition(sk1,sk2)),complement(complement(sk3)))),complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3)))))) != complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3)))))
| join(complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))),complement(join(complement(composition(sk1,sk2)),complement(complement(sk3))))) != complement(join(complement(composition(sk1,sk2)),complement(complement(sk3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_103,negated_conjecture,
join(X1,complement(join(X2,composition(sk1,X1)))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_99]),c_0_47]) ).
cnf(c_0_104,plain,
join(composition(X1,X2),composition(X1,complement(X2))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_100,c_0_30]) ).
cnf(c_0_105,plain,
converse(composition(top,converse(X1))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_84,c_0_65]) ).
cnf(c_0_106,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_101]),c_0_20]),c_0_101]) ).
cnf(c_0_107,negated_conjecture,
join(complement(X1),complement(composition(sk1,X1))) = complement(composition(sk1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_45]),c_0_22]) ).
cnf(c_0_108,negated_conjecture,
( join(complement(join(complement(composition(sk1,sk2)),complement(complement(sk3)))),complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3)))))) != complement(join(complement(composition(sk1,sk2)),complement(complement(sk3))))
| join(complement(join(complement(composition(sk1,sk2)),complement(complement(sk3)))),complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3)))))) != complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))) ),
inference(rw,[status(thm)],[c_0_102,c_0_22]) ).
cnf(c_0_109,negated_conjecture,
complement(composition(sk1,X1)) = join(complement(X1),complement(converse(composition(top,sk1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_106]),c_0_107]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_109]),c_0_40]),c_0_34]),c_0_109]),c_0_34]),c_0_99]),c_0_40]),c_0_44]),c_0_109]),c_0_34]),c_0_99]),c_0_40]),c_0_109]),c_0_40]),c_0_34]),c_0_109]),c_0_34]),c_0_99]),c_0_40]),c_0_44]),c_0_109]),c_0_40]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL030-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 04:04:27 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 131.70/19.82 % Version: 3.5.1
% 131.70/19.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 131.70/19.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 131.70/19.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 131.70/19.82 % Starting new_bool_3 with 300s (1) cores
% 131.70/19.82 % Starting new_bool_1 with 300s (1) cores
% 131.70/19.82 % Starting sh5l with 300s (1) cores
% 131.70/19.82 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 805430 completed with status 0
% 131.70/19.82 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 131.70/19.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 131.70/19.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 131.70/19.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 131.70/19.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 131.70/19.82 % No SInE strategy applied
% 131.70/19.82 % Search class: FUHPM-FFMF21-DFFFFFNN
% 131.70/19.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 131.70/19.82 % Starting SubtermCWHack with 136s (1) cores
% 131.70/19.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 131.70/19.82 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 131.70/19.82 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 131.70/19.82 % Starting new_bool_3 with 136s (1) cores
% 131.70/19.82 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 805436 completed with status 0
% 131.70/19.82 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 131.70/19.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 131.70/19.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 131.70/19.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 131.70/19.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 131.70/19.82 % No SInE strategy applied
% 131.70/19.82 % Search class: FUHPM-FFMF21-DFFFFFNN
% 131.70/19.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 131.70/19.82 % Starting SubtermCWHack with 136s (1) cores
% 131.70/19.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 131.70/19.82 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 131.70/19.82 % Preprocessing time : 0.001 s
% 131.70/19.82 % Presaturation interreduction done
% 131.70/19.82
% 131.70/19.82 % Proof found!
% 131.70/19.82 % SZS status Unsatisfiable
% 131.70/19.82 % SZS output start CNFRefutation
% See solution above
% 131.70/19.82 % Parsed axioms : 18
% 131.70/19.82 % Removed by relevancy pruning/SinE : 0
% 131.70/19.82 % Initial clauses : 18
% 131.70/19.82 % Removed in clause preprocessing : 1
% 131.70/19.82 % Initial clauses in saturation : 17
% 131.70/19.82 % Processed clauses : 9136
% 131.70/19.82 % ...of these trivial : 4999
% 131.70/19.82 % ...subsumed : 2659
% 131.70/19.82 % ...remaining for further processing : 1478
% 131.70/19.82 % Other redundant clauses eliminated : 0
% 131.70/19.82 % Clauses deleted for lack of memory : 0
% 131.70/19.82 % Backward-subsumed : 0
% 131.70/19.82 % Backward-rewritten : 395
% 131.70/19.82 % Generated clauses : 621192
% 131.70/19.82 % ...of the previous two non-redundant : 456009
% 131.70/19.82 % ...aggressively subsumed : 0
% 131.70/19.82 % Contextual simplify-reflections : 0
% 131.70/19.82 % Paramodulations : 621192
% 131.70/19.82 % Factorizations : 0
% 131.70/19.82 % NegExts : 0
% 131.70/19.82 % Equation resolutions : 0
% 131.70/19.82 % Disequality decompositions : 0
% 131.70/19.82 % Total rewrite steps : 2481830
% 131.70/19.82 % ...of those cached : 2209265
% 131.70/19.82 % Propositional unsat checks : 0
% 131.70/19.82 % Propositional check models : 0
% 131.70/19.82 % Propositional check unsatisfiable : 0
% 131.70/19.82 % Propositional clauses : 0
% 131.70/19.82 % Propositional clauses after purity: 0
% 131.70/19.82 % Propositional unsat core size : 0
% 131.70/19.82 % Propositional preprocessing time : 0.000
% 131.70/19.82 % Propositional encoding time : 0.000
% 131.70/19.82 % Propositional solver time : 0.000
% 131.70/19.82 % Success case prop preproc time : 0.000
% 131.70/19.82 % Success case prop encoding time : 0.000
% 131.70/19.82 % Success case prop solver time : 0.000
% 131.70/19.82 % Current number of processed clauses : 1066
% 131.70/19.82 % Positive orientable unit clauses : 930
% 131.70/19.82 % Positive unorientable unit clauses: 134
% 131.70/19.82 % Negative unit clauses : 0
% 131.70/19.82 % Non-unit-clauses : 2
% 131.70/19.82 % Current number of unprocessed clauses: 444565
% 131.70/19.82 % ...number of literals in the above : 444565
% 131.70/19.82 % Current number of archived formulas : 0
% 131.70/19.82 % Current number of archived clauses : 413
% 131.70/19.82 % Clause-clause subsumption calls (NU) : 2
% 131.70/19.82 % Rec. Clause-clause subsumption calls : 2
% 131.70/19.82 % Non-unit clause-clause subsumptions : 1
% 131.70/19.82 % Unit Clause-clause subsumption calls : 8566
% 131.70/19.82 % Rewrite failures with RHS unbound : 311
% 131.70/19.82 % BW rewrite match attempts : 20858
% 131.70/19.82 % BW rewrite match successes : 1845
% 131.70/19.82 % Condensation attempts : 0
% 131.70/19.82 % Condensation successes : 0
% 131.70/19.82 % Termbank termtop insertions : 22932045
% 131.70/19.82 % Search garbage collected termcells : 5
% 131.70/19.82
% 131.70/19.82 % -------------------------------------------------
% 131.70/19.82 % User time : 18.080 s
% 131.70/19.82 % System time : 0.625 s
% 131.70/19.82 % Total time : 18.705 s
% 131.70/19.82 % Maximum resident set size: 3648 pages
% 131.70/19.82
% 131.70/19.82 % -------------------------------------------------
% 131.70/19.82 % User time : 89.911 s
% 131.70/19.82 % System time : 3.187 s
% 131.70/19.82 % Total time : 93.098 s
% 131.70/19.82 % Maximum resident set size: 4608 pages
% 131.70/19.82 % E exiting
%------------------------------------------------------------------------------